A generalization of the löwdin orthogonalization

The Löwdin orthonormalized set consists of those unique orthonormal functions which minimize the quantity Σ i ∫|g i — f i | 2 dv , i.e., the sum of the squared distances in the Hilbert space between each initial function f f and a corresponding function g g of the orthonormal set. In this paper, the Löwdin orthogonalization is extended to a more general transformation. The new transformation also minimizes the sum Σ i ∫|g i — f i | 2 dv dv , but the overlap matrix of the resultant functions g g is an arbitrary positive definite matrix in contrast to the unit matrix in the Löwdin orthogonalization. The new orbital set may be useful as a basis set for some many‐electron problems in which the smallness of the sum Σ i ∫|g i — f i | 2 dv and a particular form of the overlap matrix are requested at the same time.